Vectors and Matrices for AI
Understand vectors and matrices as the language AI uses to store and transform data
A taste of a lesson
What does it mean when people say a word is a vector of 768 numbers?
It means a model represents each word, or piece of text, as a list of 768 numbers, an arrow in a 768 dimensional space. You cannot picture that, but the idea is the same as in two dimensions: words with similar meanings end up as arrows pointing in similar directions. The individual numbers usually do not mean anything on their own; the pattern across all of them carries the meaning. Quick check in 2D: which is closer to (3, 4), the vector (6, 8) or (4, -3)? Think about direction.
Written by the teacher as an example. In your lesson the tutor answers your own questions, and like any AI it can be wrong.
What you will be able to do
- Represent data points and embeddings as vectors
- Add and scale vectors and compute their length
- Read matrix shapes and index notation correctly
- Describe a dataset as a matrix of examples and features
- Explain transpose and the identity matrix
Lesson plan
- 1 Vectors as lists and arrows See a vector as both a list of numbers and an arrow. Start
- 2 Adding and scaling Add vectors and multiply them by numbers. Start
- 3 Length and unit vectors Compute a vector's length and normalise it. Start
- 4 Embeddings Understand embeddings as vectors where similar things sit close. Start
- 5 Matrices as tables Read matrix shapes and entries. Start
- 6 Transpose and identity Use the transpose and the identity matrix. Start
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About this tutor
A beginner tutor that introduces the two objects behind almost every AI model. You will see vectors as lists of numbers and as arrows, add and scale them, measure their length, and learn why a word or an image can be represented as a vector called an embedding. Then you meet matrices as tables of data and as transformations, learn shape notation, transpose and the identity matrix, and see a dataset as a matrix. All examples use small numbers you can compute by hand, with pictures described clearly. No prior linear algebra needed.
Reviews
4.7
3 ratingsSample
- Takumi H.Sample
Clear and patient. Good foundation before the dot product tutor.
- Laura S.Sample
Embeddings finally make sense at a basic level. The notation reading tips were very useful for papers.
- Bongani Z.Sample
I had avoided maths for years. The arrow pictures and tiny numbers made vectors feel friendly.
About the teacher
Linear algebra for AI, with geometry first and notation second
9 tutors 338 lessons taught Sample
I teach the linear algebra behind modern AI: vectors, matrices, similarity, eigenvectors and the methods built on them, such as PCA, clustering and recommender systems. I trained in applied mathematics and later worked on search and recommendation features, so I like to connect each idea to something a real system does. My lessons begin with pictures and small numbers you...
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